Related papers: Third derivative of the one-electron density at th…
The limit relations for the partial derivatives of the two-electron atomic wave functions at the two-particle coalescence lines have been obtained numerically using accurate CFHHM wave functions. The asymptotic solutions of the proper…
Within quantum chemistry, the electron clouds that surround nuclei in atoms and molecules are sometimes treated as clouds of probability and sometimes as clouds of charge. These two roles, tracing back to Schr\"odinger and Born, are in…
We examine the extent to which the properties of three-nucleon bound states are well-reproduced in the limit that nuclear forces satisfy Wigner's SU(4) (spin-isospin) symmetry. To do this we compute the charge radii up to next-to-leading…
Different kinds of averaging of the wavefunctions/densities of the two-electron atomic systems are investigated. Using the Pekeris-like method, the ground state wave functions $\Psi$ of the helium-like atoms with nucleus charge $1\leq…
The density dependence of the nuclear symmetry energy governs important aspects of very neutron rich systems such as heavy nuclei and their collisions, neutron stars and their mergers. Many analyses of experimental data have generated…
An analysis of the analytical solution of the Schr\"{o}dinger equation (which is a second order differential equation) for $H_2^+$ shows that the second linear independent solution of this equation is a square integrable function and…
We developed new parameterizations of local regularized finite-range pseudopotentials up to next-to-next-to-next-to-leading order (N3LO), used as generators of nuclear density functionals. When supplemented with zero-range spin-orbit and…
We consider a quantum particle moving in the one dimensional lattice Z and interacting with a indefinite sign external field v. We prove that the associated discrete Schroedinger operator H can have one or two eigenvalues, situated as below…
The polar discontinuity at the SrTiO3/LaAlO3 interface (STO/LAO) can in principle sustain an electron density of 3.3E14 cm-2 (0.5 electrons per unit cell). However, experimentally observed densities are more than an order of magnitude…
Self consistency in the analysis of transmission measurements for K^+ on several nuclei in the momentum range of 500-700 MeV/c is achieved with a "t_{eff}(rho)rho" potential and new results are derived for total cross sections. The…
We present solution of self-consistent equations for the N3LO nuclear energy density functional. We derive general expressions for the mean fields expressed as differential operators depending on densities and for the densities expressed in…
Bounds are studied for the maximum number, $N_c$, of electrons that can be bound to $K$ atoms of the total nuclear charge $Z$. It is proved that $N_c < \min\{2Z+1, 1.22Z + 3Z^{1/3}\}$ in Schr\"odinger theory. This improves Lieb's bound $N_c…
The saturation density of nuclear matter $\rho_0$ is a fundamental nuclear physics property that is difficult to predict from fundamental principles. The saturation density is closely related to the interior density of a heavy nucleus, such…
We consider eigenfunctions of a semiclassical Schr{\"o}dinger operator on an interval, with a single-well type potential and Dirichlet boundary conditions. We give upper/lower bounds on the L^2 density of the eigenfunctions that are uniform…
We construct nuclear energy density functionals in terms of derivatives of densities up to sixth, next-to-next-to-next-to-leading order (N3LO). A phenomenological functional built in this way conforms to the ideas of the density matrix…
The eigenfunctions of electronic Hamiltonians determine the stable structures and dynamics of molecules through the local distributions of their densities. In this paper an a priori upper bound for such local distributions of the densities…
Two-particle discrete Schr\"{o}dinger operators $H(k)=H_{0}(k)-V$ on the three-dimensional lattice $\Z^3,$ $k$ being the two-particle quasi-momentum, are considered. An estimate for the number of the eigenvalues lying outside of the band of…
We consider $N$-body Schr\"odinger operators with $N\geq3$ particles in dimension $d\geq 3$ in the critical case when the lowest eigenvalue coincides with the bottom of the essential spectrum of the operator. We give the asymptotic…
Accurate low and high-lying bound states of Tietz-Hua oscillator potential are presented. The radial Schr\"odinger equation is solved efficiently by means of the generalized pseudospectral method that enables optimal spatial discretization.…
Frozen Density Embedding Theory (FDET) [Wesolowski {\it Phys. Rev. A} {\bf 77}, 012504 (2008)] provides the interpretation of the eigenvalue equations for an embedded $N'$-electron wavefunction, in which the embedding operator is…